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 A264264 The length of the shortest nontrivial integral cevian of an isosceles triangle, with base of length 1 and legs of length n, that divides the base into two integral parts. 2
 4, 9, 6, 9, 36, 11, 14, 81, 16, 19, 30, 15, 24, 225, 26, 19, 48, 31, 34, 441, 36, 39, 84, 35, 44, 69, 32, 49, 900, 51, 34, 87, 56, 59, 1296, 61, 40, 141, 66, 69, 108, 49, 74, 159, 64, 53, 126, 81, 84, 2601, 86, 89, 2916, 91, 94, 147, 66, 61, 66, 101, 70, 165 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension). A nontrivial cevian is one that does not coincide with a side of the triangle. For all n, the longest nontrivial integral cevian has length n^2. LINKS Colin Barker, Table of n, a(n) for n = 2..1000 Wikipedia, Cevian Wikipedia, Isosceles triangle EXAMPLE a(4) = 6 because for legs of length 4 there are two cevians, of length 6 and 16, that divide the base into two integral parts. PROG (PARI) ceviso(n) = { my(d, L=List()); for(k=1, n^2, if(issquare(n^2+k^2-k, &d) && d!=n, listput(L, d) ) ); Vec(L) } vector(100, n, n++; ceviso(n)[1]) CROSSREFS Cf. A264263. Sequence in context: A094243 A155875 A105274 * A089390 A053667 A218072 Adjacent sequences: A264261 A264262 A264263 * A264265 A264266 A264267 KEYWORD nonn,easy AUTHOR Colin Barker, Nov 10 2015 STATUS approved

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Last modified April 12 16:49 EDT 2024. Contains 371635 sequences. (Running on oeis4.)